The hosts dominated the first half and led at the break through Jack Sowerby’s 21st-minute strike.
But on-loan midfielder Alex Gilliead equalised after a 56th-minute counter-attack before Shay McCartan put Bradford ahead seven minutes later.
It was the first time in the league this season that the Bantams had earned three points having been in a losing position and moved them to within a point of third-placed Blackburn.
McCall said: “It was a great win to start the new year. There were some really big performances in difficult conditions and it was a great turnaround.
“We have not come from a goal behind this season, so that is another box ticked and a great three points.
“It was about doing the dirty bits right and we did not do that in the opening 10 minutes, we didn’t clear our lines, we tried to clear from positions we shouldn’t.
“Jordy Hiwula should have scored (for them) early on and they got a goal which they deserved on the run of play but we grew back into it.
“With the quality we have going forward we were confident we could get goals, we got two and keeping the clean sheet in the second half was the key.”
Fleetwood head coach Uwe Rosler was not letting the blown lead take the gloss off his side’s festive form.
Town could not build on back-to-back wins at Oldham and Bury but Rosler was pleased with what he saw from his side.
Rosler said: “I think it was a very good performance, the best we have had in a long, long time, especially in the first half.
“Unfortunately we were only up 1-0 at the break, we should have been up higher. We created chances, played good football offensively and defensively. It was very good.
“We knew what was coming second half. I said just overcome the first 20 minutes because I fancied us in terms of what we had on the bench and what we could add.
“Bradford put pressure on us but they had only two shots on goal and two goals, a little bit harsh because the goals were self-inflicted.
“We lost that game, the opposition did not win it, we lost it.
“For the first we had a corner, either the ball goes in the box or you make a tactical foul and take a yellow card.
“The second is a set-piece where people are losing their man. We had that all season and we are not learning quick enough and it costs us games.
“Overall I’m very happy with the level we have played. In general I am happy with the festive period.”
Port Vale boss Neil Aspin is expected to choose from an unchanged squad for the home game against Exeter.